Question

select the correct answer from each drop - down menu. consider parallelogram abcd, where m∠abc = 135° and the length of diagonal ac is 41 units. note: figure not drawn to scale use the figure and given information to complete the statements. m∠bcd = ° (drop - down options: 270, 45, 90, 135) the length of segment cd is units. the length of segment ae is units.

Explanation:

Step1: Find $\angle BCD$

In a parallelogram, consecutive angles are supplementary. So $\angle ABC + \angle BCD = 180^\circ$.
$\angle BCD = 180^\circ - 135^\circ = 45^\circ$

Step2: Find length of $CD$

In a parallelogram, opposite sides are equal. $AB = CD$, and $AB=7$ units.
$CD = 7$ units

Step3: Find length of $AE$

In a parallelogram, diagonals bisect each other, so $AE = \frac{1}{2}AC$.
$AE = \frac{1}{2} \times 41 = 20.5$ units

Answer:

• $m\angle BCD = 45^\circ$
• The length of segment CD is 7 units.
• The length of segment AE is 20.5 units.